Question
Find roots of polynomial $$ p(x) = 12x^2+3x $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= -\dfrac{ 1 }{ 4 } \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ 3x }$ from $ 12x^2+3x $ and solve two separate equations:
$$ \begin{aligned} 12x^2+3x & = 0\\[1 em] \color{blue}{ 3x }\cdot ( 4x+1 ) & = 0 \\[1 em] \color{blue}{ 3x = 0} ~~ \text{or} ~~ 4x+1 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 2:
To find the second zero, solve equation $ 4x+1 = 0 $
$$ \begin{aligned} 4x+1 & = 0 \\[1 em] 4 \cdot x & = -1 \\[1 em] x & = - \frac{ 1 }{ 4 } \end{aligned} $$This page was created using
Polynomial Roots Calculator